This article is cited in 6 scientific papers (total in 6 papers)
The spaces of meromorphic Prym differentials on a finite Riemann surface
A. A. Kazantsevaa, V. V. Chueshevb
a Gorno-Altaisk State University, Faculty of Mathematics, Gorno-Altaisk
b Kemerovo State University, Faculty of Mathematics, Kemerovo
In the previous articles the second author started constructing a general theory of multiplicative functions and Prym differentials on a compact Riemann surface for arbitrary characters. Function theory on compact Riemann surfaces differs substantially from that on finite Riemann surfaces. In this article we start constructing a general function theory on variable finite Riemann surfaces for multiplicative meromorphic functions and differentials. We construct the forms of all elementary Prym differentials for arbitrary characters and find the dimensions of, and also construct explicit bases for, two important quotient spaces of Prym differentials. This yields the dimension of and a basis for the first holomorphic de Rham cohomology group of Prym differentials for arbitrary characters.
Teichmüller space of finite Riemann surfaces, Prym differential, vector bundle, character group, Jacobian variety, multiplicative Weierstrass point.
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Siberian Mathematical Journal, 2012, 53:1, 72–86
A. A. Kazantseva, V. V. Chueshev, “The spaces of meromorphic Prym differentials on a finite Riemann surface”, Sibirsk. Mat. Zh., 53:1 (2012), 89–106; Siberian Math. J., 53:1 (2012), 72–86
Citation in format AMSBIB
\by A.~A.~Kazantseva, V.~V.~Chueshev
\paper The spaces of meromorphic Prym differentials on a~finite Riemann surface
\jour Sibirsk. Mat. Zh.
\jour Siberian Math. J.
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O. A. Sergeeva, “The Poincare Series and Operators of Duality for Multiplicative Automorphic Forms”, J. Math. Sci., 205:3 (2015), 445–454
M. I. Tulina, “Single-valued differentials and special divisors of Prym differentials”, Siberian Math. J., 54:4 (2013), 731–745
M. I. Tulina, V. V. Chueshev, “Prym Differentials on a Variable Compact Riemann Surface”, Math. Notes, 95:3 (2014), 418–433
A. A. Kazanceva, “Single-Valued $q$-Differentials on Variable Finite Riemann Surface”, J. Math. Sci., 213:6 (2016), 857–867
O. A. Chuesheva, “Prym differentials with matrix characters on a finite Riemann surface”, Siberian Math. J., 56:3 (2015), 549–556
E. V. Semenko, “Prym differentials as solutions to boundary value problems on Riemann surfaces”, Siberian Math. J., 57:1 (2016), 124–134
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